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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ιιι be given.
Let x4 of type ιιι be given.
Let x5 of type ιιι be given.
Let x6 of type ιιι be given.
Assume H0: ∀ x7 . prim1 x7 x0∀ x8 . prim1 x8 x0x3 x7 x8 = x5 x7 x8.
Assume H1: ∀ x7 . prim1 x7 x0∀ x8 . prim1 x8 x0x4 x7 x8 = x6 x7 x8.
Apply explicit_Field_E with x0, x1, x2, x3, x4, explicit_Field x0 x1 x2 x5 x6.
Assume H2: explicit_Field x0 x1 x2 x3 x4.
Assume H3: ∀ x7 . prim1 x7 x0∀ x8 . prim1 x8 x0prim1 (x3 x7 x8) x0.
Assume H4: ∀ x7 . prim1 x7 x0∀ x8 . prim1 x8 x0∀ x9 . prim1 x9 x0x3 x7 (x3 x8 x9) = x3 (x3 x7 x8) x9.
Assume H5: ∀ x7 . prim1 x7 x0∀ x8 . prim1 x8 x0x3 x7 x8 = x3 x8 x7.
Assume H6: prim1 x1 x0.
Assume H7: ∀ x7 . prim1 x7 x0x3 x1 x7 = x7.
Assume H8: ∀ x7 . prim1 x7 x0∃ x8 . and (prim1 x8 x0) (x3 x7 x8 = x1).
Assume H9: ∀ x7 . prim1 x7 x0∀ x8 . prim1 x8 x0prim1 (x4 x7 x8) x0.
Assume H10: ∀ x7 . prim1 x7 x0∀ x8 . prim1 x8 x0∀ x9 . prim1 x9 x0x4 x7 (x4 x8 x9) = x4 (x4 x7 x8) x9.
Assume H11: ∀ x7 . prim1 x7 x0∀ x8 . prim1 x8 x0x4 x7 x8 = x4 x8 x7.
Assume H12: prim1 x2 x0.
Assume H13: x2 = x1∀ x7 : ο . x7.
Assume H14: ∀ x7 . prim1 x7 x0x4 x2 x7 = x7.
Assume H15: ∀ x7 . prim1 x7 x0(x7 = x1∀ x8 : ο . x8)∃ x8 . and (prim1 x8 x0) (x4 x7 x8 = x2).
Assume H16: ∀ x7 . prim1 x7 x0∀ x8 . prim1 x8 x0∀ x9 . prim1 x9 x0x4 x7 (x3 x8 x9) = x3 (x4 x7 x8) (x4 x7 x9).
Apply explicit_Field_I with x0, x1, x2, x5, x6 leaving 14 subgoals.
Let x7 of type ι be given.
Assume H17: prim1 x7 x0.
Let x8 of type ι be given.
Assume H18: prim1 x8 x0.
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